基于保险人自留风险约束下的最优再保险策略研究
摘
要
自然风险、意外的发生一直影响着社会发展与进步，为了降低这类突发风险对社会
的影响，保险的思想应运而生。随着经济的不断发展，社会财富与资产价值的持续增长，
保险公司业务量急剧增加，相应的承保总风险越来越大，尤其是当一些极端事件（比如
影响巨大的自然灾害：台风、海啸、地震等）发生时，保险公司独自承担这类极大的赔
偿额可能会造成公司的财务困境，严重则导致破产。为了防范这种尾部风险，再保险公
司应运而生，再保险的诞生给保险公司承保巨额风险时提供了一种思路，同时带来了降
低责任，稳定经营等优势。
目前，国内外有关最优再保险问题的前沿研究中，大多是站在再保险人的角度考虑
再保险模型中可能存在的约束条件，多数学者认为再保险公司风险的承受能力有上限或
防范道德风险的需求，往往都是对分出损失函数设定上限，而忽视了保险人对自留风险
的承担能力，实务中再保险公司可以根据需要调节自己的承保比例或进行再一次的分出
控制自己的承保风险。基于此，本文基于保险人角度，将控制保险人的风险作为约束条
件考虑最优再保险问题。
根据保险人的约束条件不同，本文建立了两种模型。在模型一中考虑保险人尾部风
险约束下，以保险人的保费最小化为目标函数，在广义的一般再保险形式中求解最优的
参数，对于保险人事先给定的置信水平与王氏保费准则中的扭曲函数，可以得到一个临
界点，当保险人的风险承受水平大于该值时，最优再保险为以该点为免赔额的比例再保
险，反之最优再保险形式为停止损失再保险。在模型二中以保险人自留风险限额为约束
条件，在无限维的最优化问题中求最优的再保险形式。其中 VaR风险度量下得到的最优
再保险策略为三层的分层再保险，当保险人的置信水平较小或保费原理的安全负荷较大
时，最优策略为为停止损失再保险；TVaR风险度量下的最优再保险策略为停止损失再
保险，其最优免赔额与保险人的自留风险上限有关。
最后，本文分别给出了保险人风险度量下不同置信水平以及损失分别服从轻尾分布
和重尾分布下相应的数值例子，对各种情况下的最优解给出了相应的说明与解释。数值
例子证明在该模型下求解出来的最优解具有一定的经济意义。
关键词：VaR；TVaR；自留风险限额；王氏保费原理
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Abstract
Abstract
The occurrence of natural risks and accidents has always affected social development and
progress. In order to reduce the impact of such sudden risks on society, the idea of insurance
came into being. With the rapid growth of insurance companies (such as earthquakes and
tsunamis), the total value of insurance companies will increase sharply, especially with the
continuous development of natural disasters, which may cause more and more serious impact
on the total financial value of insurance companies. In order to prevent this tail risk, reinsurance
companies came into being. The birth of reinsurance provides an idea for insurance companies
to underwrite huge risks, and brings advantages such as reducing liability and stable operation.
At present, most domestic and foreign literatures on optimal reinsurance strategies
consider the possible constraints in the reinsurance model from the perspective of the reinsurer.
Most scholars believe that in order to prevent moral hazard or take into account the risk
tolerance of the reinsurer, they are often setting an upper limit on the derivation function, while
ignoring the insurer’s own risk-bearing capacity. In practice, reinsurance can adjust its own
underwriting ratio according to needs or perform another divergence to control its own
underwriting risk. Based on this, this article considers the insurer’s point of view and considers
the optimal reinsurance problem with the control of the insurer’s risk as a constraint.
According to the constraints of the insurer, two models are established in this thesis.
Considering the tail risk constraints of the insurer in Model 1, the insurer’s premium is
minimized as the objective function, and the optimal parameters are solved in a generalized
general reinsurance form. For the insurer’s predetermined confidence level and Wang’s
premium criterion when the insurer’s risk tolerance level is greater than this value, the optimal
reinsurance is reinsurance in proportion to the deductible, otherwise the optimal form of
reinsurance is stop loss reinsurance. In the second model, the insurer’s own risk limit is used as
a constraint, and the optimal reinsurance form is sought in an infinite-dimensional optimization
problem. The optimal reinsurance strategy obtained under the VaR risk measurement is a three-
layer hierarchical reinsurance. In some special cases, it is stop loss reinsurance. The optimal
reinsurance strategy under the TVaR risk measurement is stop loss reinsurance, and its optimal
deductible is related to the upper limit of the insurer's own risk.
Finally, this thesis gives the corresponding numerical examples under the light-tailed
distribution and the thick-tailed distribution, and provides corresponding explanations and
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基于保险人自留风险约束下的最优再保险策略研究
explanations for the optimal solutions in various situations. Numerical examples prove that the
optimal solution solved under this model has certain economic significance.
Key Words: Value-at-Risk; Tail Value-at-Risk; Retained risk limit; Wang's premium
principle
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